Intersections of Hirzebruch–Zagier Divisors and CM Cycles
Authors: Howard, Benjamin, Yang, Tonghai
Free Preview- Develops new methods in explicit arithmetic intersection theory
- Develops new techniques for the study of Shimura varieties and automorphic forms, central objects in modern number theory
- Proves new cases of conjectures of S. Kudla
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- About this book
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This monograph treats one case of a series of conjectures by S. Kudla, whose goal is to show that Fourier of Eisenstein series encode information about the Arakelov intersection theory of special cycles on Shimura varieties of orthogonal and unitary type. Here, the Eisenstein series is a Hilbert modular form of weight one over a real quadratic field, the Shimura variety is a classical Hilbert modular surface, and the special cycles are complex multiplication points and the Hirzebruch-Zagier divisors. By developing new techniques in deformation theory, the authors successfully compute the Arakelov intersection multiplicities of these divisors, and show that they agree with the Fourier coefficients of derivatives of Eisenstein series.
- Reviews
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From the reviews:
“The reviewer recommends this beautiful monograph to anyone interested in the circle of conjecture proposed by Kudla et al., particularly from the point of view of arithmetic geometry. The work contains many useful references and intricate proofs that do not appear elsewhere, and is likely to be extremely useful to future progress in the area.” (Jeanine Van Order, Zentralblatt MATH, Vol. 1238, 2012)
- Table of contents (6 chapters)
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Introduction
Pages 1-9
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Linear Algebra
Pages 11-24
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Moduli Spaces of Abelian Surfaces
Pages 25-41
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Eisenstein Series
Pages 43-63
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The Main Results
Pages 65-84
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Table of contents (6 chapters)
- Download Preface 1 PDF (76.7 KB)
- Download Sample pages 1 PDF (195.2 KB)
- Download Table of contents PDF (61.5 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Intersections of Hirzebruch–Zagier Divisors and CM Cycles
- Authors
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- Benjamin Howard
- Tonghai Yang
- Series Title
- Lecture Notes in Mathematics
- Series Volume
- 2041
- Copyright
- 2012
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-642-23979-3
- DOI
- 10.1007/978-3-642-23979-3
- Softcover ISBN
- 978-3-642-23978-6
- Series ISSN
- 0075-8434
- Edition Number
- 1
- Number of Pages
- VIII, 140
- Topics
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